Do 2 female parakeets get along in the same cage? How about 2 Males?

Both can get along fine and happyily, but it can depend ont he bird as well, sometimes you get a rare budgie that doesn't want to share a cage with another and give up the food/water or toys to the other.

I know poeple with two males and other with two or more females all living happily in a cage together. Getting a same gender couple means you don't run the risk of unwanted breeding, two males means you don't even have to worry about random egg laying.
If you have two females they will be fine. It will be ugly if you have two males due to they will end up killing each other. It's best to have Male and Female or Female and Female.
I think it's always or most of the time the same with animals..if you're going to have two males, they should have been put together from the start as babies, but if it's two females, i dont think it's a problem.
The short answer is yes. Either way they should be fine. Just monitor the behavior at first because you could always get the weird one that wants to live alone.

In the wild keets live in large flocks. They like it that way. Just remember that the more keets you get, the noisier they are.
Yes, two males will fight. While they might not kill one another, one will eventually be bullied to the point of ill health and will be generally unhappy.

Two females can live together (usually.) You should still watch for bullying (beyond normal play behavior) and make sure the cage is big enough so they have room to romp and don't squabble for space or out of boredom.
i have 3 females and 2 males in one big cage and they are fine
parakeets are flock animals. in the wild they live and travel in flocks. they do pick mates, but its more like a best friend thing. 2 boys or 2 girls can choose to be mates. you may put 2 females in the same cage if they are used to being around each other, otherwise, they might not get along. same with males.
I have 3 male birds and 2 females in the same cage but the bigger male likes to chase the other 2 males around and trys to bite them. It just depends on the birds personality.

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